Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T, class U>
inline bool chkmax(T& a, U b) {
  return (a < b) ? (a = b, true) : false;
}
template <class T, class U>
inline bool chkmin(T& a, U b) {
  return (a > b) ? (a = b, true) : false;
}
template <class T>
inline vector<T> uniq(vector<T> vec) {
  sort((vec).begin(), (vec).end()),
      vec.erase(unique((vec).begin(), (vec).end()), end(vec));
  return vec;
}
void Main();
int32_t main(int argc, char** argv) {
  ios::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  int T = 1;
  while (T--) Main();
}
const int Move[][2] = {{1, 0}, {0, 1}};
void Main() {
  int n;
  cin >> n;
  vector<pair<int, int> > ans(1, {1, 1});
  for (int i = 1; i < n; i++) {
    pair<int, int> cur;
    cur.first = ans.back().first + Move[i & 1][0];
    cur.second = ans.back().second + Move[i & 1][1];
    ans.push_back(cur);
  }
  cout << max(ans.back().first, ans.back().second) << "\n";
  for (auto& x : ans) cout << x.first << " " << x.second << "\n";
}